Let's say I want to generate a random real number.

I can take a fair 10-sided die and generate the (infinite number of) digits. I can toss a fair coin to decide whether the number should be positive or negative.

Question is: what method do I use to insert the decimal point?

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    $\begingroup$ You can use any method of selecting a natural number randomly. For instance, flip a coin until you get heads, and count the number of tails. There is no way to do this so it is uniform, because there in no uniform probability on the reals. $\endgroup$ – Thomas Andrews Aug 19 '16 at 17:54
  • $\begingroup$ @ThomasAndrews I think you mean "on the natural numbers" (but what you say is true too). Post as an answer? $\endgroup$ – Ethan Bolker Aug 19 '16 at 17:57
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    $\begingroup$ There is no uniform probably on the reals and no uniform probability on the natural numbers. @EthanBolker $\endgroup$ – Thomas Andrews Aug 19 '16 at 18:13

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